The Rolex site has only some of what's available. Go to an authorized dealer and look, and ask to see the catalogue. There are tons of other Rolex options. Here's a site that shows the dial options:
www.oysterworld.de
The DateJust has many more options that the Date, plus different sizes. There is really no DateJust in 34mm aside from some extremely costs Special Edition DJS: the normal sizes are 26, 31, 36, and now the new 41. So if you're set on 34 it's a Date, or an Air King.
You asked about the date feature on the watch: the magnification of the cyclops--the little glass bubble over the date area--is a Rolex classic feature. If you want a date on a watch, the DJ or Date is certainly the way to go.
About bracelets, the two main ones for the DJ are the Jubilee and the Oyster. There's also a more expensive bracelet called the President. The Jubilee is not offered on the Date, just the DJ (of the two you're considering; it's also available on other Rolexes).
To learn more, start visiting dealers and playing with the watches and talking to salespeople. You can go several times before buying: they're used to that.
My 31mm: